## Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly. On the other hand, the weekly syllabus contained in the Homework assignments page will always be accurate.

WkLecturesSections in TextTopics
16/23Presentation of the course
6/24Chap.2Composition laws
26/27Chap.3, Chap.4Groups
6/29Chap.5Subgroups
7/01Chap.5Generators, cyclic groups
37/06Chap.6Functions
7/07Complements on subgroups, discussion of Quiz 1 (solution)
7/08Chap.7Bijections
47/11Chap.12, Chap.14Equivalence relations, homomorphisms
7/13Chap. 15Cosets, normal subgroups, quotient groups
7/14Chap.7More on quotients
7/15Chap.16The First Isomorphism Theorem
57/18Chap.8Symmetric groups (Prof. Tanabe)
7/20Chap. 11Cyclic groups and their subgroups - Review session (Prof. Muetzel)
7/21Midterm ExamSolution
7/22Chap. 13Lagrange's Theorem and application (S. Chari)
67/25More on the order and index of subgroups
7/27Chap. 8The alternating group
7/28Wrap-up discussion on groups
7/29Chap. 17Rings
78/01Chap. 18Morphisms and ideals
8/03Chap. 18Properties of ideals
8/04Discussion on rings
8/05Chap. 19Quotient rings, fields
88/08Chap. 20Fields of fractions, complex numbers
8/10Chap. 22, Chap. 24Arithmetic in $\mathbb{Z}$ and $F[X]$
8/11Complements and discussion on rings
8/12Chap. 22, Chap. 25Factorization in $\mathbb{Z}$ and $F[X]$
98/15Chap. 26Irreducibility in polynomial rings
8/17Chap. 27Fields extensions
8/18Quiz 2 (solution)
8/19Chap. 28, Chap. 29Degrees of fields extensions
108/22Wrap-up
8/24Chap. 30Application: ruler and compass constructions
8/29Final Examinationdue by noon (solution)